"""simple docstring"""


def      lowerCamelCase_					(   __lowerCAmelCase=2_8123							)				->   int:




						'''simple docstring'''



						lowerCamelCase__   =[1] * (limit + 1)

						for i in range(2  ,       int(limit**0.5							) + 1							):
												sum_divs[i * i] += i
												for k in range(i + 1  ,       limit // i + 1							):
																		sum_divs[k * i] += k + i

						lowerCamelCase__   =set()
						lowerCamelCase__   =0

						for n in range(1  ,       limit + 1							):
												if sum_divs[n] > n:
																		abundants.add(__lowerCAmelCase							)

												if not any((n - a in abundants) for a in abundants							):
																		res += n

						return res


if __name__ == "__main__":
	print(solution())



"""simple docstring"""


from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase = False							)				->   list[float]:




						'''simple docstring'''



						if radian_mode:
												return [magnitude * cos(__lowerCAmelCase							), magnitude * sin(__lowerCAmelCase							)]
						return [magnitude * cos(radians(__lowerCAmelCase							)							), magnitude * sin(radians(__lowerCAmelCase							)							)]





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase = 10**-1							)				->   bool:




						'''simple docstring'''



						lowerCamelCase__   =cross(__lowerCAmelCase  ,       __lowerCAmelCase							)
						lowerCamelCase__   =sum(__lowerCAmelCase							)
						return abs(__lowerCAmelCase							) < eps


if __name__ == "__main__":
	# Test to check if it works
	a				=array(
	    [
	        polar_force(718.4, 180 - 30),
	        polar_force(879.54, 45),
	        polar_force(100, -90),
	    ]
	)

	a				=array([[0, 0], [0, 0], [0, 0]])

	assert in_static_equilibrium(forces, location)

	# Problem 1 in image_data/2D_problems.jpg
	a				=array(
	    [
	        polar_force(30 * 9.81, 15),
	        polar_force(215, 180 - 45),
	        polar_force(264, 90 - 30),
	    ]
	)

	a				=array([[0, 0], [0, 0], [0, 0]])

	assert in_static_equilibrium(forces, location)

	# Problem in image_data/2D_problems_1.jpg
	a				=array([[0, -2000], [0, -1200], [0, 1_5600], [0, -1_2400]])

	a				=array([[0, 0], [6, 0], [10, 0], [12, 0]])

	assert in_static_equilibrium(forces, location)

	import doctest

	doctest.testmod()


